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  • Textbook
  • © 1993

Noncommutative Algebra

Authors:

  1. Benson Farb

    1. Department of Mathematics, Princeton University, Princeton, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. R. Keith Dennis

    1. Department of Mathematics, Cornell University, Ithaca, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Graduate Texts in Mathematics (GTM, volume 144)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xiv
    PDF

  2. The Core Course

    1. Front Matter

      Pages 1-1
      PDF

    2. Background Material

      • Benson Farb, R. Keith Dennis
      Pages 3-27
      PDF

    3. Semisimple Modules & Rings and the Wedderburn Structure Theorem

      • Benson Farb, R. Keith Dennis
      Pages 29-56
      PDF

    4. The Jacobson Radical

      • Benson Farb, R. Keith Dennis
      Pages 57-79
      PDF

    5. Central Simple Algebras

      • Benson Farb, R. Keith Dennis
      Pages 81-108
      PDF

    6. The Brauer Group

      • Benson Farb, R. Keith Dennis
      Pages 109-148
      PDF

  3. Selected Topics

    1. Front Matter

      Pages 149-149
      PDF

    2. Primitive Rings and the Density Theorem

      • Benson Farb, R. Keith Dennis
      Pages 151-159
      PDF

    3. Burnside’s Theorem and Representations of Finite Groups

      • Benson Farb, R. Keith Dennis
      Pages 161-175
      PDF

    4. The Global Dimension of a Ring

      • Benson Farb, R. Keith Dennis
      Pages 177-183
      PDF

    5. The Brauer Group of a Commutative Ring

      • Benson Farb, R. Keith Dennis
      Pages 185-198
      PDF

  4. Supplementary Exercises

    1. Front Matter

      Pages 199-199
      PDF

    2. Supplementary Exercises

      • Benson Farb, R. Keith Dennis
      Pages 201-214
      PDF

  5. Back Matter

    Pages 215-226
    PDF
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About this book

About This Book This book is meant to be used by beginning graduate students. It covers basic material needed by any student of algebra, and is essential to those specializing in ring theory, homological algebra, representation theory and K-theory, among others. It will also be of interest to students of algebraic topology, functional analysis, differential geometry and number theory. Our approach is more homological than ring-theoretic, as this leads the to many important areas of mathematics. This ap­ student more quickly proach is also, we believe, cleaner and easier to understand. However, the more classical, ring-theoretic approach, as well as modern extensions, are also presented via several exercises and sections in Chapter Five. We have tried not to leave any gaps on the paths to proving the main theorem- at most we ask the reader to fill in details for some of the sideline results; indeed this can be a fruitful way of solidifying one's understanding.
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Keywords

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Authors and Affiliations

  • Department of Mathematics, Princeton University, Princeton, USA

    Benson Farb

  • Department of Mathematics, Cornell University, Ithaca, USA

    R. Keith Dennis

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Bibliographic Information

  • Book Title: Noncommutative Algebra

  • Authors: Benson Farb, R. Keith Dennis

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-0889-1

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1993

  • Hardcover ISBN: 978-0-387-94057-1Published: 20 August 1993

  • Softcover ISBN: 978-1-4612-6936-6Published: 30 September 2012

  • eBook ISBN: 978-1-4612-0889-1Published: 06 December 2012

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: XIV, 226

  • Topics: Algebra

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Download book PDF

Buy it now

Softcover Book USD 69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 89.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

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